If what Giuliani says is true, what Mueller told him was that he would follow the DOJ guidelines which say that that you can't indict a sitting president. So, yes, technically that does mean Mueller is not going to indict Trump, but the Fox headline suggests that he's exonerated Trump while the other shows that it's the technical DOJ rule not the merits of the case.

I'm pretty sure the Nixon Grand Jury that returned indictments on a boatload of his staffers had Nixon as an un-indicted co-conspirator. Trump and his followers probably wouldn't care about that and they'd carry on about witch hunts and the like. But it would hardly be an exoneration.